Let's say that you invent a time machine and go back to time (t) in the past. Now, if someone at time (t - 1 hour) measured the entire energy in the universe and arrived at figure (e), when he measures again at time (t + 1 hour) the total energy in the universe will have increased by a factor of (<your mass at time of departure from present> * c^2). Energy will have been created.

I suppose you could look at it in terms of an equilibrium over all time--i.e. if you take eternity as a whole, the disappearance of your energy from the future would cancel out its appearance at time (t). But it would make these laws basically useless, I think, if you have to take into account any future or past events and how they might affect your current measurements.

However, you can fix this problem. Causality won't be violated if the area you take the energy from is sufficiently far away from where you're acting. If I take mass from the Alpha Centauri system to solve the energy problem 5 years ago, if I just live out 5 years causality gets violated as our light cones merge.

If I take the energy from a star 6 billion light years away, I can go back in time 5,999,999,999.999 years and causality won't be violated as said star couldn't have had an effect on Earth for me to remove.

Essentially this is like time travel in a bubble.

As for "Back to the Future" style, that's actually between theories. Doc talks about multiple timelines, essentially describing the Multiverse model; I think Biff picks up a gambling book from the future and instead of being Marty's families' stooge, he becomes a rich bastard and like owns the planet or something odd. However, people disappearing from the timeline and Marty getting weak when he was unlikely to be born is more Newtonian as in a multiverse you can't effect your own past.

It's possible it's Quantum Time Travel, as it's predicted some particles act in time loops; essentially they ditch our time and go back a year and then carry on like normal and no one even notices, because they're actually there 1 second after they go back in time but we can't tell they're actually 1 year and 1 second older not just 1 second older. It's very odd.

In Quantum, violating the law of thermodynamics (AFAIK) doesn't seem to have an effect. As far as I understood what I read your latter assumption seems to be on par. However, I think if you sufficiently altered the entropy of a system, that's when causality would kick in. Merely having more mass in a system doesn't make much different, as long as that small amount of mass doesn't start causing asteroids to crash into the planet and black holes to form... or the death of your grandfather. Like the predicted particles, going back in time doesn't cause buildings to collapse or people to die, so the universe lets it slide. I think if we went sending neutron bombs back in time to wipe out Hitler, then there would be major causality problems for multiple reasons namely there'd never have been a Hitler to nuke!

So overall I'd say the BttF style of time travel was obviously the writers' confusion between two distinct theories of time travel. Multiverse fits the universal effects, but quantum fits the characters' effects.

But there can be events where every single version of you is guaranteed to Infinite-Hotel to the universe next door and kill Grandfather[n+1]--basically the same thing, as your grandfather does indeed end up dead.